This project is directed at developing and using physical and mathematical methodologies to understand integrative aspects of complex cellular processes. Emphasis has been on studying the functioning of multicomponent, supramolecular entities such as composite membranes and elements of cytoskeletal networks, particularly to understand their involvement in cellular organization and cell shape. Related in vitro reconstitution studies of purified cell components also have been undertaken. These investigations oftentimes employ unusual physical instrumentation, in part to examine the general utility of such devices for biological research. For example, we have been using fluorescence correlation spectroscopy (FCS)to investigate tubulin ring polymers induced by certain small peptides that are being evaluated as antimitotic agents. We have combined FCS and analytical ultracentrifugation of the cryptophycin-tubulin rings to test thories and computational code that provide values of hydrodynamic coefficients for complex-shaped particles. In addition, we have undertaken FCS investigations to study the transport of biological macromolecules through complex polymer networks and have employed small angle light scattering (SALS) to understand shape changes that occur when polyelectrolyte gels are subject to electric fields. We also have implemented time-dependent total internal reflectance microscopy (TIRFM) to investigate how multicomponent antigen receptor complexes on Jurkat T-cells form and move after antigen presentation, and are developing other fluorescence based techniques to study living cells. We also conduct research to understand how the biogenesis of such clathrin-coated vesicles occurs. Physical models based on notions of statistical mechanics and thermodynamics have enabled us to determine the mechanical role of assembly proteins (APs) in mediating the formation of clathrin cages. Our analysis demonstrated that the binding of APs prevents the legs of neighboring triskelions from sliding with respect to each other when they interwind to form the struts of a completed cage. In addition, our work confirmed that coats containing only clathrin and APs are unlikely to bend portions of a typical plasma membrane into small vesicles whose size is similar to that of clathrin coated vesicles. In a related investigation, we have used dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS) to discern, for example, that triskelions in solution have an intrinsic pucker whose geometrical form is close to that inferred previously by cryoelectron microscopic examination of intact baskets. DLS measurements indicate only a weak dependence of pucker on pH and other solution conditions, supporting the notion that clathrin triskelia, when inserted into cages and coats, change their shape to conform to the geometry of the coat at the cost of relatively small strain energy. Addionally, we have developed a method based on weak contact-mode atomic force microscopy (AFM) to estimate the rigidity of the composite structure (plasma membrane, clathrin, and associated proteins) that embodies a vesicle. Preliminary results indicate that the rigidity of the composite is approximately ten times that of either the membrane or clathrin lattice, consistent with a model where the clathrin cage is joined to the membrane by discrete elastic elements. Also, increasing evidence suggests that the binding of clathrin-associated proteins to PIP2 and other phosphoinositides (PIs) plays an important role in vesicle formation, perhaps by inducing curvature changes in the lipid membrane. We have employed mathematical and computational methods to examine a biochemical scheme for regulation of PI signaling that includes actions of PI kinases and phosphatases, phospholipase C, small g-proteins, and phosphatidic acid production. The feedback and feed-forward character of cyclic pathways of PI mettabolism suggests their possible roles as biochemical switches for vesicle formation and other cellular processes. We have focused initially on gradient sensing in immune and amoeboid cells, but anticipate using a variant of the model to understand how PIs might influence the inception of endocytic vesicles.